David's distance

Geometry Level 4

Let ABCDABCD be a rectangle such that AB=5AB=5 and BC=12BC=12. There exist two distinct points X1X_1 and X2X_2 on BCBC such that AX1D=AX2D=90\angle AX_1D=\angle AX_2D=90^\circ. Suppose that dd is the distance from X1X_1 to X2X_2. What is d2d^2?

This problem is posed by David A.

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